Labour's Bill Shorten became the first leader of a major Australian political party to back a bill to overturn a national ban on gay marriage.

Gay rights advocates fear government MPs will be reluctant to back the bill as it would be seen as a political victory for Mr Shorten over Prime Minister Tony Abbott, a former Roman Catholic seminarian and a staunch opponent of marriage equality.

Mr Shorten told parliament the law would not compel religious clerics to officiate at same-sex marriages.

He urged Mr Abbott to allow MPs in his ruling Liberal Party a free vote, rather than require them to back the party's line in opposing marriage equality.

"Our laws should be a mirror reflecting our great and generous country and our free, inclusive society," Mr Shorten said on introducing the bill.

His deputy Tanya Plebersek seconded the bill, after no government MP took up the offer to perform that official function as a gesture of bipartisanship support.

Mr Abbott said his government was focused on Australia's economic and national security rather than marriage law reform.

"Let's see where the community debate goes. There's a range of views on both sides of the issue," he told reporters.

There is no timetable set for a vote, but Labour hopes it will happen this year.

Labour Senate leader Penny Wong, who is in a lesbian relationship, said last month's referendum when 62% of Irish voters called for their constitution to be changed to allow same-sex marriage was an important trigger for a similar debate in Australia.

Opinion polls show most Australians support gay marriage. Gay rights advocates say Australia is now the only English-speaking developed country to ban same-sex marriage after the Irish vote.

In 2004, the parliament changed the law with the unanimous support of the ruling conservative coalition and Labour to make it clear that only a man and a woman could marry.

But Labour has since changed its stance.

A move to allow same-sex marriage proposed by a junior Labour MP in 2012 while Labour was in government was soundly rejected by the House of Representatives, 98 votes to 42.

Labour MPs were allowed to vote according to their consciences, while Liberals were required to oppose marriage equality.

Mr Abbott says he has yet to decide whether his party's MPs would he allowed a free vote when the issue next comes up in parliament.

Analysts say that since Mr Abbott's authority was weakened by a leadership challenge from within his party in February, he may be unlikely to anger marriage equality advocates within government ranks by denying them a free vote.

Even with all MPs allowed a free vote, gay rights advocates say the result would be close.